Theories

Title of theory.

Dialogue

First encounter dialogue
"Oh, there you are."
"I thought you'd all but forgotten me. How sweet."
"Good to know that a skinny little heretic can still turn heads."

First encounter, second dialogue
"Hm? Oh…you're not one of them, are you?"
"Accept my apologies, for mistaking you for one of those leeches."
"So, what business have you here?"
"This is a land of monstrosities. And I am no exception."

Choice: Offer help/Do not help her

Offer help
"You're here to save me…?"
"But I am guilty. A wretched child of the Abyss."
"Is that something you can forgive?"

First encounter in Firelink Shrine
"Ahh, there you are."
"As I said, I am Karla. And am grateful to you."
"Now, what shall we do."
"The only thing that might interest you is my sorcery."
"Although my dark arts are a detestable sort."
"That wouldn't interest you, would it?"

Ask to learn dark sorceries
"Hm."
"You're a wicked one, aren't you?"
"Very well. Humans are of the dark, and you are no different."
"Some may avert their eyes, but the truth remains the truth."
"Be careful though. Few humans are privy to this knowledge."
"Let it be a secret, KEPT between you and I…" (She says 'kept' between "…secret, between…")

Decline

First "Talk" option
"There is one thing that you should know."
"There is a darkness within man, and I am afraid you will peer into it."
"Whether the fear will spark self-reflection, or a ruinous nostalgia…"
"…is up to you entirely."
"Fear not, your choice will bring you no scorn."

Sources

Karla's Ashes
Umbral ash of Karla. With this, the shrine handmaid will prepare new items.
The spurned child of the Abyss never dies, but phases in and out of its fringes. Only, there is no one to search for her any longer.

Karla's Pointed Hat
Hat of the dark witch Karla.
A pointed hat is the signature of a heretical sorceress. Karla, however always kept if close.

Karla's Coat
Coat of the dark witch Karla.
This stained coat is torn and odorous, telling of a long journey and even longer imprisonment.
It would be madness to wear such a thing.